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The Planar Dimer Model, continued

by
Alex Bloemendal
|
University of Toronto
Time: 13:00 (Wednesday, Mar. 17, 2010)Location: BA6183, Bahen Center, 40 St George StAbstract:
In this sequel to last week's talk, we'll take a closer look at the entropy functional as we recap the proof of the limit shape theorem of Cohn, Kenyon and Propp. Along the way we'll encounter the ergodic Gibbs measures, which describe the local states, and mention Sheffield's classification theorem. Kenyon, Okounkov and Sheffield later identified the local entropy as the Legendre dual of the Ronkin function of a polynomial that encodes the lattice structure; analyzing the inverse Kasteleyn matrix, they were then able to give a satisfying explanation of the different phases of local states. If there is time, we'll touch on Kenyon and Okounkov's solution of the variational problem, the underlying conformal structure, and the loci of the spatial phase transitions.